A shrinking lemma for random forbidding context languages

Walt, Andries van der; Ewert, Sigrid

doi:10.1016/s0304-3975(98)00160-1

Cited by 20 publications

(9 citation statements)

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“…Note also that it is known that the language families generated by (λ-free) restricted context-free rewriting systems with nonterminals coupled only with + (only with −, respectively) are weaker than the general case. Specifically, they are included in the language families generated by random context grammars without appearance checking (also called permitting grammars) and forbidding random context grammars, respectively, which are known to be properly included in the family of recursive languages or in the family of random context (matrix) languages if λ-productions are or are not allowed, respectively (see [8,10,9] and Fig. 2 for an overview of the language hierarchy).…”

Section: Resultsmentioning

confidence: 99%

“…This characterization results in some new normal forms for random context grammars and their variants discussed in the literature (see [3][4][5][6][7]), as well as for matrix grammars. As it is not hard to see that any restricted context-free rewriting system can be thought of as a (very simple type of) random context grammars, it immediately follows that nonterminals coupled with both + and − are required because it is well known that random context grammars with all permitting (forbidding, respectively) sets being empty characterize a proper subfamily of the family of (even) recursive languages (see [8] and also [9,10]). …”

Section: Introductionmentioning

confidence: 99%

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Simple restriction in context-free rewriting

Masopust

2010

Journal of Computer and System Sciences

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Many rewriting systems with context-free productions and with controlled derivations have been studied. On one hand, these systems preserve the simplicity of applications of context-free productions and, on the other hand, they increase the generative power to cover more aspects of natural and programming languages. However, with λ-productions, many of these systems are computationally complete. It gives rise to a natural question of what are the simplest restrictions of the derivation process of context-free grammars to obtain the universal power. In this paper, we present such a simple restriction introducing so-called restricted context-free rewriting systems. These systems are contextfree grammars with a function assigning a nonterminal coupled with + or − to each nonterminal. A production is applicable if it is applicable as a context-free production and if the symbol assigned to the left-hand side of the production is coupled with +, then this symbol has to appear in the sentential form, while if coupled with −, it must not appear in the sentential form. This restriction is simpler than most of the other restrictions, since the context conditions are assigned to nonterminals, not to productions, and their type is the simplest possible -a nonterminal.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simple restriction in context-free rewriting

Masopust

2010

Journal of Computer and System Sciences

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“…A generalization of RCGs for phrase-structure rules can be found in [13]. The generative capacity and several descriptional properties of RCGs can be found in [10], [13], [16], [46], and [47].…”

Section: Szilard Languages Of Random Context Grammarsmentioning

confidence: 99%

On the Complexity of Szilard Languages of Regulated Grammars

Cojocaru

Mäkinen

2011

Theoretical Aspects of Computing – ICTAC 2011

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The regulated rewriting mechanism is one of the most efficient methods to augment the Chomsky hierarchy with a large variety of language classes. In this paper we investigate the derivation process in regulated rewriting grammars such as matrix grammars, programmed grammars, and random context grammars by studying their Szilard languages. We prove that Szilard languages associated with unrestricted derivations in these grammars can be recognized in logarithmic time and space by indexing alternating Turing machines. Hence, these classes of Szilard languages belong to the U E * -uniform N C 1 class [40]. In general, leftmost Szilard languages of regulated rewriting grammars can be recognized in logarithmic space and square logarithmic time. Hence, these classes of languages belong to N C 2 [40].

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“…Such a production can rewrite a nonterminal provided that no symbol from its attached set occurs to the left of the rewritten nonterminal in the current sentential form. Here is the difference compared to the random forbidding context grammars (see [4,5]) because, in random forbidding context grammars, symbols from the attached set are looked up in the whole sentential form. As the key topic of investigation, we concentrate our attention on the generative power of cooperating distributed grammar systems with left-forbidding components with respect to the number of components, derivation modes, and erasing productions.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, formal language theory has discussed some random forbidding/permitting context grammars that are not as powerful as random context grammars (see [5,6], respectively), and some cooperating distributed grammar systems with random forbidding/permitting context components working in the terminal derivation mode that are as powerful as random context grammars (see [7,8], respectively). In view of these results, the results of the present paper are of some interest because the cooperation increases the generative power of cooperating distributed grammar systems with left-forbidding components from the power of context-free grammars to the power of context sensitive or phrase structure grammars.…”

Section: Introductionmentioning

confidence: 99%

Left-forbidding cooperating distributed grammar systems

Goldefus

Masopust

Meduna

2010

Theoretical Computer Science

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a b s t r a c tA left-forbidding grammar, introduced in this paper, is a context-free grammar, where a set of nonterminal symbols is attached to each context-free production. Such a production can rewrite a nonterminal provided that no symbol from the attached set occurs to the left of the rewritten nonterminal in the current sentential form. The present paper discusses cooperating distributed grammar systems with left-forbidding grammars as components and gives some new characterizations of language families of the Chomsky hierarchy. In addition, it also proves that twelve nonterminals are enough for cooperating distributed grammar systems working in the terminal derivation mode with two left-forbidding components (including erasing productions) to characterize the family of recursively enumerable languages.

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A shrinking lemma for random forbidding context languages

Cited by 20 publications

References 2 publications

Simple restriction in context-free rewriting

Simple restriction in context-free rewriting

On the Complexity of Szilard Languages of Regulated Grammars

Left-forbidding cooperating distributed grammar systems

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